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Search: id:A082958
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| A082958 |
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Number of symmetric short bushes with n edges. I.e. number of ordered trees with n edges, no vertices of outdegree 1, and which are symmetrical with respect to the vertical axis passing through the root. |
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+0
2
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| 0, 1, 1, 1, 2, 3, 4, 7, 10, 17, 25, 43, 64, 111, 167, 291, 442, 773, 1183, 2075, 3196, 5619, 8702, 15329, 23852, 42085, 65755, 116181, 182186, 322287, 507020, 897859, 1416594, 2510901, 3971887, 7045915, 11171924, 19832947, 31514404, 55982893
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discrete Math., 204, 1999, 73-112.
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FORMULA
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G.f.=[(1-z)(1+z^2)-(1+z)sqrt(1-2z^2-3z^4)]/[2z(z^3+z^2+z-1)]
a(n) has antiparity of A007814(n+1), i.e. a(n) mod 2 = A035263(n+1). - Ralf Stephan, Feb 21 2004
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CROSSREFS
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Adjacent sequences: A082955 A082956 A082957 this_sequence A082959 A082960 A082961
Sequence in context: A136570 A119016 A082766 this_sequence A060166 A053634 A094863
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 26 2003
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